MPI-I-95-1-013
Efficient computation of implicit representations of sparse graphs (revised version)
Arikati, Srinivasa R. and Maheshwari, Anil and Zaroliagis, Christos D.
June 1995, 16 pages.
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Status: available - back from printing
The problem of finding an implicit representation for a graph
such that vertex adjacency can be tested quickly is
fundamental to all graph algorithms. In particular, it
is possible to represent sparse graphs on $n$ vertices
using $O(n)$ space such that vertex adjacency is tested
in $O(1)$ time. We show here how to construct such a
representation efficiently by providing simple and optimal
algorithms, both in a sequential and a parallel setting.
Our sequential algorithm runs in $O(n)$ time.
The parallel algorithm runs in $O(\log n)$ time using
$O(n/{\log n})$ CRCW PRAM processors, or in $O(\log n\log^*n)$
time using $O(n/\log n\log^*n)$ EREW PRAM processors.
Previous results for this problem
are based on matroid partitioning and thus have a high complexity.
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URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1995-1-013
BibTeX
@TECHREPORT{ArikatiMaheshwariZaroliagis95,
AUTHOR = {Arikati, Srinivasa R. and Maheshwari, Anil and Zaroliagis, Christos D.},
TITLE = {Efficient computation of implicit representations of sparse graphs (revised version)},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPI-I-95-1-013},
MONTH = {June},
YEAR = {1995},
ISSN = {0946-011X},
}